(y-18)(y-18)-1=0

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Solution for (y-18)(y-18)-1=0 equation: 


Simplifying
(y + -18)(y + -18) + -1 = 0

Reorder the terms:
(-18 + y)(y + -18) + -1 = 0

Reorder the terms:
(-18 + y)(-18 + y) + -1 = 0

Multiply (-18 + y) * (-18 + y)
(-18(-18 + y) + y(-18 + y)) + -1 = 0
((-18 * -18 + y * -18) + y(-18 + y)) + -1 = 0
((324 + -18y) + y(-18 + y)) + -1 = 0
(324 + -18y + (-18 * y + y * y)) + -1 = 0
(324 + -18y + (-18y + y2)) + -1 = 0

Combine like terms: -18y + -18y = -36y
(324 + -36y + y2) + -1 = 0

Reorder the terms:
324 + -1 + -36y + y2 = 0

Combine like terms: 324 + -1 = 323
323 + -36y + y2 = 0

Solving
323 + -36y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(17 + -1y)(19 + -1y) = 0


Subproblem 1
Set the factor '(17 + -1y)' equal to zero and attempt to solve:

Simplifying
17 + -1y = 0

Solving
17 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + -1y = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1y = 0 + -17
-1y = 0 + -17

Combine like terms: 0 + -17 = -17
-1y = -17

Divide each side by '-1'.
y = 17

Simplifying
y = 17

Subproblem 2
Set the factor '(19 + -1y)' equal to zero and attempt to solve:

Simplifying
19 + -1y = 0

Solving
19 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-19' to each side of the equation.
19 + -19 + -1y = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1y = 0 + -19
-1y = 0 + -19

Combine like terms: 0 + -19 = -19
-1y = -19

Divide each side by '-1'.
y = 19

Simplifying
y = 19
Solution
y = {17, 19}

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